I have a new client that requires three reports from my data. One must be legal/landscape, the second is letter/landscape, and the last one is letter/portrait. How do I tell FMP to do three different formats?

You need a separate report layout for each variant.

I have a separate report layout for each one. When I apply the page size to one report layout the other two layouts take on that new size. How do I keep the proper size assigned to each layout?

Print Setups are not layout specific, but rather file specific. That is, you must change the entire file's print setup when you run a report. This is accomplished by using the Print Setup script step in any report printing script.

So when I go to print the three reports I have to stop between printing each one so I can select the proper paper size and orientation. Or else I have to write a script just to print them.

I may have a script question about this later.

Yes, you need to go to Print Setup before you print, either manually via a script -- Print Setup (Restore).